In eQTL studies, the relationship between gene expression levels and genotypes is under systematic investigation. A major issue in inferring eQTL is that a few number of factors, such as unobserved covariates, experimental artifacts, and unknown environmental perturbations, may confound the observed expression levels. This may both mask real associations, and lead to spurious associations. The key challenge accounting for the confounding effects is that these factors may not be directly and completely observable, and thus remain hidden. Noticing that the effects of a few of unobserved confounding variables can be captured by a low-rank structure, this problem can be formulated as low-rank approximation in the setting of sparse regression. An efficient algorithm is available for large-scale data analysis and its performance has been demonstrated in both simulated and real data.